We study the physical content of two block-alternating infinite products A (K, d) and B (K, d), identifying the parameter K as a distance scale. Three results emerge from this identification, without any relativistic or field-theoretic assumption. First, the logarithmic K-derivative of A satisfies d/dK log A = (d/4) K^-2 + O (K^-3), establishing a Newtonian gravitational potential with coupling GM = d/4. The null point K = 1/2 coincides exactly with the Schwarzschild radius rS = d/2, and the determinant identity det MA + det MB = 0 corresponds to the on-shell geodesic condition v² = GM/r for circular orbits. Second, extending K to the complex plane via K = 1/2 + r exp (itheta), the matrix MB satisfies the exact identity det MB (1/2 + r exp (itheta) ) = -4r² exp (2i*theta). This provides a structure analogous to the Wick rotation: the Minkowski and Euclidean regimes appear as two faces of a single analytic expression, with K = 1/2 as the rotation axis. Third, the product family Aᵃ × Bᵇ carries gravitational coupling GM = (a+2b) d/4, forming a discrete spectrum with quantum number n = a+2b. Setting G = 1/4 gives M = d: the mass of the gravitational source equals the block length d, which is a positive integer by construction. This is a form of mass quantization arising purely from the combinatorial structure of the sign alternation.
Masanori Fujii (Wed,) studied this question.